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Popular >

derivative of sqrt(x^2-2x+5)

Solution

\frac{d}{d x} (x^{2} - 2 x + 5)

Solution

\frac{x - 1}{x ^{2} - 2 x + 5}

Solution steps

\frac{d}{d x} (x^{2} - 2 x + 5)

Apply the chain rule:

\frac{1}{2 x ^{2} - 2 x + 5} \frac{d}{d x} (x^{2} - 2 x + 5)

= \frac{1}{2 x ^{2} - 2 x + 5} \frac{d}{d x} (x^{2} - 2 x + 5)

\frac{d}{d x} (x^{2} - 2 x + 5) = 2 x - 2

= \frac{1}{2 x ^{2} - 2 x + 5} (2 x - 2)

Simplify

\frac{1}{2 x ^{2} - 2 x + 5} (2 x - 2) : \frac{x - 1}{x ^{2} - 2 x + 5}

= \frac{x - 1}{x ^{2} - 2 x + 5}

Popular Examples

integral of 1/((a^2+x^2)^{3/2)}

\int \frac{1}{( a ^{2} + x ^{2} ) ^{\frac{3}{2}}} d x

derivative of (x+4)(x^2-4)derivative of

(x + 4) (x^{2} - 4)

integral of (sqrt(x))/((1+x)^2)

\int \frac{x}{( 1 + x ) ^{2}} d x

area x^2-1,[-1,2]area

x^{2} - 1, [- 1, 2]

(d^2)/(dx^2)(2csc(x))

\frac{d ^{2}}{d x ^{2}} (2 csc (x))

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x^2-2x+5) ?
The derivative of sqrt(x^2-2x+5) is (x-1)/(sqrt(x^2-2x+5))
What is the first derivative of sqrt(x^2-2x+5) ?
The first derivative of sqrt(x^2-2x+5) is (x-1)/(sqrt(x^2-2x+5))